What is N9: Standard form?

Standard form writes a number as A10^n, where 1≤ A<10 and n is an integer. A positive index moves the decimal point right to make a large ordinary number; a negative index moves it left to make a small one.

How many marks are N9 questions worth?

In verified past-paper appearances, N9 questions on Edexcel GCSE Maths 1MA1 have been worth 2–4 marks.

Which past exam papers has N9 appeared in?

N9 has appeared in 23 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Calculate with and interpret standard form A × 10^n, where 1 ≤ A < 10 and n is an integer

Q: How many marks are N9 questions worth?

In verified past-paper appearances, N9 questions on Edexcel GCSE Maths 1MA1 have been worth 2–4 marks.

Q: Which past exam papers has N9 appeared in?

N9 has appeared in 23 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Standard form

Worked answers, methods and verified real exam appearances for N9 on Edexcel GCSE Maths 1MA1.

Explanation

Standard form writes a number as $A\times10^n$ , where $1\leq A<10$ and $n$ is an integer. A positive index moves the decimal point right to make a large ordinary number; a negative index moves it left to make a small one.
For multiplication, multiply the $A$ values and add the indices; for division, divide the $A$ values and subtract the indices.
For addition or subtraction, first rewrite the terms with the same power of $10$ .
Finally normalise the coefficient so it lies in the required interval.
Examiners can award method marks for correct index work before normalisation.

Worked example

Work out $\dfrac{3.6\times10^{-4}+7.5\times10^{-5}}{1.5\times10^3}$ in standard form.

1.Use a common power: $3.6\times10^{-4}+0.75\times10^{-4}=4.35\times10^{-4}$ .
2.Divide coefficients and subtract indices: $(4.35\div1.5)\times10^{-4-3}$ .
3.Evaluate and check the coefficient: $2.9\times10^{-7}$ .

Answer: $2.9\times10^{-7}$ .

Common mistakes

Don't leave $24\times10^4$ as the final answer even though $24$ is not between $1$ and $10$ .
Don't add the indices when dividing powers of $10$ .
Don't add coefficients whose powers of $10$ have not first been made equal.

Exam tip

Circle the final coefficient and check $1\leq A<10$ before submitting any standard-form answer.

Worked practice

Tier 1 · Easy

Write

0.000072

in standard form.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$7.2\times10^{-5}$	1	Move the decimal point $5$ places right to make $7.2$ . Moving right gives a negative power, so $0.000072=7.2\times10^{-5}$ .

Tier 2 · Standard

Work out

(6\times10^7)(4\times10^{-3})

. Give your answer in standard form.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$2.4\times10^5$	2	Multiply the factors and add the indices: $6\times4=24$ and $10^7\times10^{-3}=10^4$ . Thus the product is $24\times10^4=2.4\times10^5$ .

Tier 3 · Hard

Work out

\dfrac{3.6\times10^{-4}+7.5\times10^{-5}}{1.5\times10^3}

. Give your answer in standard form.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$2.9\times10^{-7}$	4	Express the numerator with a common power: $3.6\times10^{-4}+0.75\times10^{-4}=4.35\times10^{-4}$ . Divide the factors and subtract the indices: $(4.35/1.5)\times10^{-4-3}=2.9\times10^{-7}$ .

Tier 1 · Easy

Write

4\,530\,000

in standard form.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$4.53\times10^6$	1	Move the decimal point $6$ places left to make $4.53$ , so $4\,530\,000=4.53\times10^6$ .

Tier 2 · Standard

Work out

\dfrac{8.4\times10^6}{2.1\times10^2}

. Write your answer in the form

A\times10^n

, where

1\leq A<10

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$4\times10^4$	2	Divide the numbers and subtract the indices: $(8.4\div2.1)\times10^{6-2}=4\times10^4$ .

Tier 3 · Hard

Machine A makes

4.5\times10^5

components and machine B makes

0.62\times10^6

components. Work out how many more components machine B makes. Give your answer in standard form.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$1.7\times10^5$ components	3	Write both amounts with the same power: $0.62\times10^6=6.2\times10^5$ . The difference is $(6.2-4.5)\times10^5=1.7\times10^5$ components.

Tier 2 · Standard

A parcel has mass

3.75\times10^4

grams. Another parcel has mass

8600

grams. Work out their total mass in standard form.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$4.61\times10^4$ grams	3	$8600=0.86\times10^4$ . The total is therefore $(3.75+0.86)\times10^4=4.61\times10^4$ grams.

Tier 3 · Hard

Each tray contains

2.4\times10^3

screws. There are

3.5\times10^2

trays. After inspection,

6.7\times10^4

screws are rejected. Work out the number of screws that are not rejected. Give your answer in standard form.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$7.73\times10^5$ screws	4	The trays contain $(2.4\times10^3)(3.5\times10^2)=8.4\times10^5$ screws. Write the rejected amount as $0.67\times10^5$ . The number left is $(8.4-0.67)\times10^5=7.73\times10^5$ screws.

Tier 3 · Hard

A survey stores

4.2\times10^7

readings. Each reading uses

1.5\times10^{-3}

MB. After

1.1\times10^4

MB is deleted, the remaining data is shared equally between

8\times10^2

drives. Work out the amount on each drive. Give your answer in standard form.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$6.5\times10^1$ MB	4	The readings use $(4.2\times10^7)(1.5\times10^{-3})=6.3\times10^4$ MB. After deletion, $6.3\times10^4-1.1\times10^4=5.2\times10^4$ MB remains. Each drive receives $\dfrac{5.2\times10^4}{8\times10^2}=0.65\times10^2=6.5\times10^1$ MB.

Q10

Tier 3 · Hard

Factory X makes

3.2\times10^4

clips each day for

18

days. Factory Y makes

5.5\times10^5

clips in total. Work out how many more clips factory X makes than factory Y. Give your answer in standard form.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$2.6\times10^4$ clips	4	Factory X makes $(3.2\times10^4)\times18=57.6\times10^4=5.76\times10^5$ clips. The difference is $5.76\times10^5-5.5\times10^5=0.26\times10^5=2.6\times10^4$ clips.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-06	2F	Q27	2	Allowed	Foundation	QP MS
2022-11	3H	Q9	3	Allowed	Higher	QP MS
2019-11	2H	Q7	2	Allowed	Higher	QP MS
2022-11	3F	Q29	3	Allowed	Foundation	QP MS
2019-06	2H	Q8	2	Allowed	Higher	QP MS
2024-06	3F	Q23	4	Allowed	Foundation	QP MS
2023-11	3F	Q20	2	Allowed	Foundation	QP MS
2023-06	3F	Q28	4	Allowed	Foundation	QP MS
2022-06	1H	Q4	4	Non-calculator	Higher	QP MS
2024-11	3H	Q2	2	Allowed	Higher	QP MS
2019-11	3H	Q7	3	Allowed	Higher	QP MS
2024-11	3F	Q18	2	Allowed	Foundation	QP MS
2024-06	3H	Q19	3	Allowed	Higher	QP MS
2019-06	3H	Q11	3	Allowed	Higher	QP MS
2019-11	3F	Q28	3	Allowed	Foundation	QP MS
2021-11	3F	Q23	4	Allowed	Foundation	QP MS
2022-06	1F	Q26	4	Non-calculator	Foundation	QP MS
2019-11	2F	Q27	2	Allowed	Foundation	QP MS
2024-11	2F	Q27	2	Allowed	Foundation	QP MS
2024-06	3H	Q2	4	Allowed	Higher	QP MS
2021-11	3H	Q3	4	Allowed	Higher	QP MS
2024-11	2H	Q8	2	Allowed	Higher	QP MS
2023-11	3H	Q1	2	Allowed	Higher	QP MS

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